Biophysics of somersault and arm sets in trampolining John Mitchell Thanks to Lisa Withey + Jack Mitchell for performance

Introduction In depth calculations are not included in this presentation. These are available on request. The data presented is approximately 50% from direct video measurement and 50% from calculation. Where calculations have been used a number of body weight and size approximations have been used and actual numbers will vary with performer. This is intended as a first draft for more in depth analysis in a suitable sports science department. The next slide presents data measured using motionview 7.2 showing body angles on last contact Vs amount of rotation generated. There is clearly good correlation for the performers used.

 a b d From the leg body angle a leg to vertical angle can be inferred And this can be used to calculate the amount of energy converted from bounce height into kinetic rotational energy (Whether this is valid to do so is up for comment) The body has to bend forward in this front somersault example to keep the Center of mass d above the Base of support Back somersault rotation seems to use a straighter body position to gain the same amount of rotation. (Noisy) Poor timed somersaults caused by pushing on the landing phase rather than in the take-off phase require a greater angle of body bend (hip displacement) as they are getting less energy from the trampoline Force Rotation vector 

To exemplify the theory that rotational energy can be calculated from the vector of Leg angle and total potential energy of the performer (assuming no extra leg forces in operation) the first thing to do was calculate the total energy gained. This has been done using a 60kg model body and is plotted below for different 10 bounce times

Assuming a straight shape for a 60kg body of 1.75m the amount of energy required per degree of rotation can be calculated. The graph below has this re-plotted in terms of the % height energy converted for different degrees of rotation assuming bounce time of 16 seconds for 10 bounces.

This graph is the least evidence based as I didn’t have good enough images. So it is essentially a theoretical graph on a load of assumptions about how vertical force from the trampoline is split by different angles of the leg. However, the next slide Shows good agreement between this and the theoretical energy used for rotation Calculated from angular velocity and mass in straight shape.

Comparison of the two methods for calculation of energy of rotation suggests that leg angle is a good predictor of the total rotation initiated and is likely to be the main factor determining the degree of rotation.

Calculation of absolute energy required for rotation in a straight shape allows us to then calculate energy used for phased tuck and pike somersaults. (with some assumptions of Moments of inertia and body size and weight) These have been plotted below vs 10 bounce time The preceding graphs all assume no extra leg push. So I wanted to check that It is possible for a gymnast to put in enough extra energy to compensate for height loss.

In order to do this the graph above was calculated for standing jump for a 60kg person.

Adult vertical jump norms GenderExcellent Above average Average Below average Poor Male>65cm60m55cm50cm<46cm Female>55cm50cm45cm40cm<36cm Clearly the range of vertical jump for most gymnasts is clearly able to produce sufficient PE to account for the degrees of height otherwise lost in somersault rotation

Arm setting What is the advantage of arm setting? Finally I wanted to examine the affect of arm set position for front somersault take off positions. The method used was to balance in different front rotation positions relating to different somersaults, then lift arms up while maintaining balance and measure the resulting body angle changes. This was done for both front and back rotation positions with the front somersault results presented here.

a b c a b c d d   Degrees  Degrees To maintain body COM above feet the body has to move 8 degrees while maintaining same leg position (degree of rotation initiation) for 107 deg starting position. Arms up therefore results in a more upright body position for the same rotation. This example uses the body angle used for triple straight front somersaults 107 and front drop 157 degrees. The chart on the next slide shows actual measured differences for an 80kg male.  degrees 160 degrees

Actual measured adjustment to maintain balance on raising arms As expected this is broadly following a sin wave trigonometric function, the actual magnitude of which will be determined by the ratio of arm and torso mass and length. A vertical arm position clearly has more effect the more rotation is initiated. The effect on body position for back somersault rotation was approximately half as much.

Conclusions for somersaulting 1. Simple application of vectors based on body angles and leg position can be used to describe trampoline somersaults 2. Conservation of energy suggests that extra leg push is therefore necessary to maintain height. Bouncing at 100% max height will therefore result in height loss. 3. A significant amount of energy is used in straight shapes and bounce time above 14 seconds appear to be a reasonable minimum for teaching more than 360 deg in this shape. 4. Arm position has a large effect on body angle while maintaining the same degree of likely somersault. 5. Degree of somersault is likely to be set predominantly by the leg angle. 6. Body angle to maintain the Centre of mass will adjust but it will not change the height gained. 7. Arm sets will therefore not change the amount of somersault but will make the body position easier to reach (more upright) for multiple somersaults 8. Height gain through an arm swing technique will give about 30 joules height gain (5cm) This is approximately the same as 50% of a tuck somersault. 9. Arm set should therefore have as much bed contact as possible to incorporate the energy from Arm swing. Vertical arms on first contact will not add to height. 10. There is good video based evidence that body to leg angle correlates with degree of rotation.